Across the country, they are signing up to be Republican precinct leaders, a position so low-level that it often remains vacant, but which comes with the ability to vote for the party executives who endorse candidates, approve platforms and decide where the party spends money.

A new group called the National Precinct Alliance says it has a coordinator in nearly every state to recruit Tea Party activists to fill the positions and has already swelled the number of like-minded members in Republican Party committees in Arizona and Nevada. Its mantra is this: take the precinct, take the state, take the party — and force it to nominate conservatives rather than people they see as liberals in Republican clothing…

“It puts in stark relief where the American people are, how they feel and what they feel,” Mr. Steele said. “It’s important for our party to appreciate and understand that so we can move toward it, and embrace it.”

Not all Republicans agree. Some say the party needs to broaden its reach, not cater to the fringe.